Abstract

A prism-pair interferometer comprising two homodyne interferometers with a common light source was developed for high-precision measurements of the refractive index of optical glasses with an uncertainty of the order of 106. The two interferometers measure changes in the optical path length in the glass sample and in air, respectively. Uncertainties in the absolute wavelength of the common light source are cancelled out by calculating a ratio between the results from the interferometers. Uncertainties in phase measurement are suppressed by a quadrature detection system. The combined standard uncertainty of the developed system is evaluated as 1.1×106.

© 2011 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]

2009 (4)

M. Pisani, “A homodyne Michelson interferometer with sub-picometer resolution,” Meas. Sci. Technol. 20, 084008(2009).
[CrossRef]

J. A. Stone, J. E. Decker, P. Gill, P. Juncar, A. Lewis, G. D. Rovera, and M. Viliesid, “Advice from the CCL on the use of unstabilized lasers as standards of wavelength: The helium–neon laser at 633 nm,” Metrologia 46, 11–18 (2009).
[CrossRef]

M. Astrua and M. Pisani, “Prism refractive index measurement at INRiM,” Meas. Sci. Technol. 20, 095305 (2009).
[CrossRef]

Y. Hori, A. Hirai, K. Minoshima, and H. Matsumoto, “High-accuracy interferometer with a prism pair for measurement of the absolute refractive index of glass,” Appl. Opt. 48, 2045–2050 (2009).
[CrossRef] [PubMed]

2005 (2)

T. Keem, S. Gonda, I. Misumi, Q. Huang, and T. Kurosawa, “Simple, real-time method for removing the cyclic error of a homodyne interferometer with a quadrature detector system,” Appl. Opt. 44, 3492–3498 (2005).
[CrossRef] [PubMed]

I. Misumi, S. Gonda, Q. Huang, T. Keem, T. Kurosawa, A. Fujii, N. Hisata, T. Yamagishi, H. Fujimoto, K. Enjoji, S. Aya, and H. Sumitani, “Sub-hundred nanometer pitch measurements using an AFM with differential laser interferometers for designing usable lateral scales,” Meas. Sci. Technol. 16, 2080–2090 (2005).
[CrossRef]

2002 (2)

2000 (1)

H. Delbarre, C. Przygodzki, M. Tassou, and D. Boucher, “High-precision index measurement in anisotropic crystals using white-light spectral interferometry,” Appl. Phys. B 70, 45–51 (2000).
[CrossRef]

1997 (1)

K. Fujii, E. R. Williams, R. L. Steiner, and D. B. Newell, “A new refractometer by combining a variable length vacuum cell and a double-pass Michelson interferometer,” IEEE Trans. Instrum. Meas. 46, 191–195 (1997).
[CrossRef]

1996 (1)

1981 (1)

1979 (1)

M. J. Downs and K. W. Raine, “An unmodulated bi-directional fringe-counting interferometer system for measuring displacement,” Precis. Eng. 1, 85–88 (1979).
[CrossRef]

1968 (1)

Astrua, M.

M. Astrua and M. Pisani, “Prism refractive index measurement at INRiM,” Meas. Sci. Technol. 20, 095305 (2009).
[CrossRef]

Aya, S.

I. Misumi, S. Gonda, Q. Huang, T. Keem, T. Kurosawa, A. Fujii, N. Hisata, T. Yamagishi, H. Fujimoto, K. Enjoji, S. Aya, and H. Sumitani, “Sub-hundred nanometer pitch measurements using an AFM with differential laser interferometers for designing usable lateral scales,” Meas. Sci. Technol. 16, 2080–2090 (2005).
[CrossRef]

Boucher, D.

H. Delbarre, C. Przygodzki, M. Tassou, and D. Boucher, “High-precision index measurement in anisotropic crystals using white-light spectral interferometry,” Appl. Phys. B 70, 45–51 (2000).
[CrossRef]

Burnett, J. H.

Ciddor, P. E.

Daimon, M.

Decker, J. E.

J. A. Stone, J. E. Decker, P. Gill, P. Juncar, A. Lewis, G. D. Rovera, and M. Viliesid, “Advice from the CCL on the use of unstabilized lasers as standards of wavelength: The helium–neon laser at 633 nm,” Metrologia 46, 11–18 (2009).
[CrossRef]

Delbarre, H.

H. Delbarre, C. Przygodzki, M. Tassou, and D. Boucher, “High-precision index measurement in anisotropic crystals using white-light spectral interferometry,” Appl. Phys. B 70, 45–51 (2000).
[CrossRef]

Downs, M. J.

M. J. Downs and K. W. Raine, “An unmodulated bi-directional fringe-counting interferometer system for measuring displacement,” Precis. Eng. 1, 85–88 (1979).
[CrossRef]

Enjoji, K.

I. Misumi, S. Gonda, Q. Huang, T. Keem, T. Kurosawa, A. Fujii, N. Hisata, T. Yamagishi, H. Fujimoto, K. Enjoji, S. Aya, and H. Sumitani, “Sub-hundred nanometer pitch measurements using an AFM with differential laser interferometers for designing usable lateral scales,” Meas. Sci. Technol. 16, 2080–2090 (2005).
[CrossRef]

Fujii, A.

I. Misumi, S. Gonda, Q. Huang, T. Keem, T. Kurosawa, A. Fujii, N. Hisata, T. Yamagishi, H. Fujimoto, K. Enjoji, S. Aya, and H. Sumitani, “Sub-hundred nanometer pitch measurements using an AFM with differential laser interferometers for designing usable lateral scales,” Meas. Sci. Technol. 16, 2080–2090 (2005).
[CrossRef]

Fujii, K.

K. Fujii, E. R. Williams, R. L. Steiner, and D. B. Newell, “A new refractometer by combining a variable length vacuum cell and a double-pass Michelson interferometer,” IEEE Trans. Instrum. Meas. 46, 191–195 (1997).
[CrossRef]

Fujimoto, H.

I. Misumi, S. Gonda, Q. Huang, T. Keem, T. Kurosawa, A. Fujii, N. Hisata, T. Yamagishi, H. Fujimoto, K. Enjoji, S. Aya, and H. Sumitani, “Sub-hundred nanometer pitch measurements using an AFM with differential laser interferometers for designing usable lateral scales,” Meas. Sci. Technol. 16, 2080–2090 (2005).
[CrossRef]

Gill, P.

J. A. Stone, J. E. Decker, P. Gill, P. Juncar, A. Lewis, G. D. Rovera, and M. Viliesid, “Advice from the CCL on the use of unstabilized lasers as standards of wavelength: The helium–neon laser at 633 nm,” Metrologia 46, 11–18 (2009).
[CrossRef]

Gonda, S.

I. Misumi, S. Gonda, Q. Huang, T. Keem, T. Kurosawa, A. Fujii, N. Hisata, T. Yamagishi, H. Fujimoto, K. Enjoji, S. Aya, and H. Sumitani, “Sub-hundred nanometer pitch measurements using an AFM with differential laser interferometers for designing usable lateral scales,” Meas. Sci. Technol. 16, 2080–2090 (2005).
[CrossRef]

T. Keem, S. Gonda, I. Misumi, Q. Huang, and T. Kurosawa, “Simple, real-time method for removing the cyclic error of a homodyne interferometer with a quadrature detector system,” Appl. Opt. 44, 3492–3498 (2005).
[CrossRef] [PubMed]

Griesmann, U.

Gupta, R.

Heydemann, P. L. M.

Hirai, A.

Hisata, N.

I. Misumi, S. Gonda, Q. Huang, T. Keem, T. Kurosawa, A. Fujii, N. Hisata, T. Yamagishi, H. Fujimoto, K. Enjoji, S. Aya, and H. Sumitani, “Sub-hundred nanometer pitch measurements using an AFM with differential laser interferometers for designing usable lateral scales,” Meas. Sci. Technol. 16, 2080–2090 (2005).
[CrossRef]

Hori, Y.

Huang, Q.

I. Misumi, S. Gonda, Q. Huang, T. Keem, T. Kurosawa, A. Fujii, N. Hisata, T. Yamagishi, H. Fujimoto, K. Enjoji, S. Aya, and H. Sumitani, “Sub-hundred nanometer pitch measurements using an AFM with differential laser interferometers for designing usable lateral scales,” Meas. Sci. Technol. 16, 2080–2090 (2005).
[CrossRef]

T. Keem, S. Gonda, I. Misumi, Q. Huang, and T. Kurosawa, “Simple, real-time method for removing the cyclic error of a homodyne interferometer with a quadrature detector system,” Appl. Opt. 44, 3492–3498 (2005).
[CrossRef] [PubMed]

Juncar, P.

J. A. Stone, J. E. Decker, P. Gill, P. Juncar, A. Lewis, G. D. Rovera, and M. Viliesid, “Advice from the CCL on the use of unstabilized lasers as standards of wavelength: The helium–neon laser at 633 nm,” Metrologia 46, 11–18 (2009).
[CrossRef]

Keem, T.

I. Misumi, S. Gonda, Q. Huang, T. Keem, T. Kurosawa, A. Fujii, N. Hisata, T. Yamagishi, H. Fujimoto, K. Enjoji, S. Aya, and H. Sumitani, “Sub-hundred nanometer pitch measurements using an AFM with differential laser interferometers for designing usable lateral scales,” Meas. Sci. Technol. 16, 2080–2090 (2005).
[CrossRef]

T. Keem, S. Gonda, I. Misumi, Q. Huang, and T. Kurosawa, “Simple, real-time method for removing the cyclic error of a homodyne interferometer with a quadrature detector system,” Appl. Opt. 44, 3492–3498 (2005).
[CrossRef] [PubMed]

Kurosawa, T.

I. Misumi, S. Gonda, Q. Huang, T. Keem, T. Kurosawa, A. Fujii, N. Hisata, T. Yamagishi, H. Fujimoto, K. Enjoji, S. Aya, and H. Sumitani, “Sub-hundred nanometer pitch measurements using an AFM with differential laser interferometers for designing usable lateral scales,” Meas. Sci. Technol. 16, 2080–2090 (2005).
[CrossRef]

T. Keem, S. Gonda, I. Misumi, Q. Huang, and T. Kurosawa, “Simple, real-time method for removing the cyclic error of a homodyne interferometer with a quadrature detector system,” Appl. Opt. 44, 3492–3498 (2005).
[CrossRef] [PubMed]

Lewis, A.

J. A. Stone, J. E. Decker, P. Gill, P. Juncar, A. Lewis, G. D. Rovera, and M. Viliesid, “Advice from the CCL on the use of unstabilized lasers as standards of wavelength: The helium–neon laser at 633 nm,” Metrologia 46, 11–18 (2009).
[CrossRef]

Masumura, A.

Matsumoto, H.

Minoshima, K.

Misumi, I.

I. Misumi, S. Gonda, Q. Huang, T. Keem, T. Kurosawa, A. Fujii, N. Hisata, T. Yamagishi, H. Fujimoto, K. Enjoji, S. Aya, and H. Sumitani, “Sub-hundred nanometer pitch measurements using an AFM with differential laser interferometers for designing usable lateral scales,” Meas. Sci. Technol. 16, 2080–2090 (2005).
[CrossRef]

T. Keem, S. Gonda, I. Misumi, Q. Huang, and T. Kurosawa, “Simple, real-time method for removing the cyclic error of a homodyne interferometer with a quadrature detector system,” Appl. Opt. 44, 3492–3498 (2005).
[CrossRef] [PubMed]

Newell, D. B.

K. Fujii, E. R. Williams, R. L. Steiner, and D. B. Newell, “A new refractometer by combining a variable length vacuum cell and a double-pass Michelson interferometer,” IEEE Trans. Instrum. Meas. 46, 191–195 (1997).
[CrossRef]

Pisani, M.

M. Astrua and M. Pisani, “Prism refractive index measurement at INRiM,” Meas. Sci. Technol. 20, 095305 (2009).
[CrossRef]

M. Pisani, “A homodyne Michelson interferometer with sub-picometer resolution,” Meas. Sci. Technol. 20, 084008(2009).
[CrossRef]

Przygodzki, C.

H. Delbarre, C. Przygodzki, M. Tassou, and D. Boucher, “High-precision index measurement in anisotropic crystals using white-light spectral interferometry,” Appl. Phys. B 70, 45–51 (2000).
[CrossRef]

Raine, K. W.

M. J. Downs and K. W. Raine, “An unmodulated bi-directional fringe-counting interferometer system for measuring displacement,” Precis. Eng. 1, 85–88 (1979).
[CrossRef]

Rovera, G. D.

J. A. Stone, J. E. Decker, P. Gill, P. Juncar, A. Lewis, G. D. Rovera, and M. Viliesid, “Advice from the CCL on the use of unstabilized lasers as standards of wavelength: The helium–neon laser at 633 nm,” Metrologia 46, 11–18 (2009).
[CrossRef]

Steiner, R. L.

K. Fujii, E. R. Williams, R. L. Steiner, and D. B. Newell, “A new refractometer by combining a variable length vacuum cell and a double-pass Michelson interferometer,” IEEE Trans. Instrum. Meas. 46, 191–195 (1997).
[CrossRef]

Stone, J. A.

J. A. Stone, J. E. Decker, P. Gill, P. Juncar, A. Lewis, G. D. Rovera, and M. Viliesid, “Advice from the CCL on the use of unstabilized lasers as standards of wavelength: The helium–neon laser at 633 nm,” Metrologia 46, 11–18 (2009).
[CrossRef]

Sumitani, H.

I. Misumi, S. Gonda, Q. Huang, T. Keem, T. Kurosawa, A. Fujii, N. Hisata, T. Yamagishi, H. Fujimoto, K. Enjoji, S. Aya, and H. Sumitani, “Sub-hundred nanometer pitch measurements using an AFM with differential laser interferometers for designing usable lateral scales,” Meas. Sci. Technol. 16, 2080–2090 (2005).
[CrossRef]

Tassou, M.

H. Delbarre, C. Przygodzki, M. Tassou, and D. Boucher, “High-precision index measurement in anisotropic crystals using white-light spectral interferometry,” Appl. Phys. B 70, 45–51 (2000).
[CrossRef]

Viliesid, M.

J. A. Stone, J. E. Decker, P. Gill, P. Juncar, A. Lewis, G. D. Rovera, and M. Viliesid, “Advice from the CCL on the use of unstabilized lasers as standards of wavelength: The helium–neon laser at 633 nm,” Metrologia 46, 11–18 (2009).
[CrossRef]

Werner, A. J.

Williams, E. R.

K. Fujii, E. R. Williams, R. L. Steiner, and D. B. Newell, “A new refractometer by combining a variable length vacuum cell and a double-pass Michelson interferometer,” IEEE Trans. Instrum. Meas. 46, 191–195 (1997).
[CrossRef]

Yamagishi, T.

I. Misumi, S. Gonda, Q. Huang, T. Keem, T. Kurosawa, A. Fujii, N. Hisata, T. Yamagishi, H. Fujimoto, K. Enjoji, S. Aya, and H. Sumitani, “Sub-hundred nanometer pitch measurements using an AFM with differential laser interferometers for designing usable lateral scales,” Meas. Sci. Technol. 16, 2080–2090 (2005).
[CrossRef]

Appl. Opt. (7)

Appl. Phys. B (1)

H. Delbarre, C. Przygodzki, M. Tassou, and D. Boucher, “High-precision index measurement in anisotropic crystals using white-light spectral interferometry,” Appl. Phys. B 70, 45–51 (2000).
[CrossRef]

IEEE Trans. Instrum. Meas. (1)

K. Fujii, E. R. Williams, R. L. Steiner, and D. B. Newell, “A new refractometer by combining a variable length vacuum cell and a double-pass Michelson interferometer,” IEEE Trans. Instrum. Meas. 46, 191–195 (1997).
[CrossRef]

Meas. Sci. Technol. (3)

I. Misumi, S. Gonda, Q. Huang, T. Keem, T. Kurosawa, A. Fujii, N. Hisata, T. Yamagishi, H. Fujimoto, K. Enjoji, S. Aya, and H. Sumitani, “Sub-hundred nanometer pitch measurements using an AFM with differential laser interferometers for designing usable lateral scales,” Meas. Sci. Technol. 16, 2080–2090 (2005).
[CrossRef]

M. Pisani, “A homodyne Michelson interferometer with sub-picometer resolution,” Meas. Sci. Technol. 20, 084008(2009).
[CrossRef]

M. Astrua and M. Pisani, “Prism refractive index measurement at INRiM,” Meas. Sci. Technol. 20, 095305 (2009).
[CrossRef]

Metrologia (1)

J. A. Stone, J. E. Decker, P. Gill, P. Juncar, A. Lewis, G. D. Rovera, and M. Viliesid, “Advice from the CCL on the use of unstabilized lasers as standards of wavelength: The helium–neon laser at 633 nm,” Metrologia 46, 11–18 (2009).
[CrossRef]

Precis. Eng. (1)

M. J. Downs and K. W. Raine, “An unmodulated bi-directional fringe-counting interferometer system for measuring displacement,” Precis. Eng. 1, 85–88 (1979).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Principle of prism-pair interferometry. Ps, sample prism; Pi, incident prism; ML, refractive index-matching liquid. Interferometer 1 detects the change of phase ( Δ ϕ 1 ) with the change in optical path length in Ps. Interferometer 2 detects the change of phase ( Δ ϕ 2 ) with the change in optical path length in air generated by translation of Ps. On the assumption that wavelength of the light source in interferometer 1 is equal to that in interferometer 2, the absolute refractive index of Ps is calculated by means of Eq. (2).

Fig. 2
Fig. 2

Signal processing of quadrature signals from interferometer 1. A PD detects one of four orthogonal interferograms. In step 1, two sinusoidal signals with a phase difference of 90 ° are obtained by subtracting the intensity of the interferograms detected by PD2 and PD4 from those of PD1 and PD3, respectively. In step 2, a Lissajous trajectory is generated by positioning the intensities of the two sinusoidal signals on the x and y axes. From the angle of the Lissajous trajectory, the change in phase ( Δ ϕ 1 ) produced by the translation of Ps is obtained. A similar process is adopted for interferometer 2.

Fig. 3
Fig. 3

Experimental setup. Each frequency factor from the orthogonally polarized two-frequency He–Ne laser separated by PBS1 is introduced into each interferometer. Both interferometers are Michelson-type homodyne interferometers with quadrature detection systems. The detection part of interferometer 2 is the same as that of interferometer 1.

Fig. 4
Fig. 4

Cyclical error of the processed quadrature signals before (a) and after (b) correction by elliptical fitting of the Lissajous trajectory. Vertical axis is the phase of the cyclical error and horizontal axis is the detection time of the quadrature signals.

Fig. 5
Fig. 5

Allan standard deviations of phase from the quadrature signals of interferometers 1 and 2, obtained during 6 h in an insulated stable environment.

Fig. 6
Fig. 6

Results of a series of measurements. Each filled circle is the average values of one set of ten continuous measurements, and the error bar corresponds to the standard deviation of the set. Ps is reset after each set of measurements and its orientation is changed after every two sets. The averaged value for all 60 measurements is 1.5154325, represented by the horizontal dotted line.

Tables (1)

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Table 1 Uncertainty Budget of the Proposed Method a

Equations (4)

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n s = n a ( Δ x 1 / Δ x 2 ) .
n s = n a ( Δ ϕ 1 / Δ ϕ 2 ) .
Δ ϕ i = 2 π N i + ε i ( i = 1 , 2 ) ,
ε i = Δ φ i + Δ ψ i ( i = 1 , 2 ) ,

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